Heterogeneous information phase space reconstruction and stability prediction of filling body–surrounding rock combination

Traditional research believes that the filling body can effectively control stress concentration while ignoring the problems of unknown stability and the complex and changeable stress distribution of the filling body–surrounding rock combination under high-stress conditions.Current monitoring data processing methods cannot fully consider the complexity of monitoring objects,the diversity of monitoring methods,and the dynamics of monitoring data.To solve this problem,this paper proposes a phase space reconstruction and stability prediction method to process heterogeneous information of backfill–surrounding rock combinations.The three-dimensional monitoring system of a large-area filling body–surrounding rock combination in Longshou Mine was constructed by using drilling stress,multipoint displacement meter,and inclinometer.Varied information,such as the stress and displacement of the filling body–surrounding rock combination,was continuously obtained.Combined with the average mutual information method and the false nearest neighbor point method,the phase space of the heterogeneous information of the filling body–surrounding rock combination was then constructed.In this paper,the distance between the phase point and its nearest point was used as the index evaluation distance to evaluate the stability of the filling body–surrounding rock combination.The evaluated distances(ED)revealed a high sensitivity to the stability of the filling body–surrounding rock combination.The new method was then applied to calculate the time series of historically ED for 12 measuring points located at Longshou Mine.The moments of mutation in these time series were at least 3 months ahead of the roadway return dates.In the ED prediction experiments,the autoregressive integrated moving average model showed a higher prediction accuracy than the deep learning models(long short-term memory and Transformer).Furthermore,the root-mean-square error distribution of the prediction results peaked at 0.26,thus outperforming the no-prediction method in 70%of the cases.

Prediction of seawater pH by bidirectional gated recurrent neural network with attention under phase space reconstruction:case study of the coastal waters of Beihai,China

Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environment.At present,the monitoring method of seawater pH has been matured.However,how to accurately predict future changes has been lacking effective solutions.Based on this,the model of bidirectional gated recurrent neural network with multi-headed self-attention based on improved complete ensemble empirical mode decomposition with adaptive noise combined with phase space reconstruction(ICPBGA)is proposed to achieve seawater pH prediction.To verify the validity of this model,pH data of two monitoring sites in the coastal sea area of Beihai,China are selected to verify the effect.At the same time,the ICPBGA model is compared with other excellent models for predicting chaotic time series,and root mean square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R2)are used as performance evaluation indicators.The R2 of the ICPBGA model at Sites 1 and 2 are above 0.9,and the prediction errors are also the smallest.The results show that the ICPBGA model has a wide range of applicability and the most satisfactory prediction effect.The prediction method in this paper can be further expanded and used to predict other marine environmental indicators.

THE STATE SPACE RECONSTRUCTION TECHNOLOGY OF DIFFERENT KINDS OF CHAOTIC DATA OBTAINED FROM DYNAMICAL SYSTEM

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.

Prediction of elevator traffic flow based on SVM and phase space reconstruction

To make elevator group control system better follow the change of elevator traffic flow (ETF) in order to adjust the control strategy,the prediction method of support vector machine (SVM) in combination with phase space reconstruction has been proposed for ETF.Firstly,the phase space reconstruction for elevator traffic flow time series (ETFTS) is processed.Secondly,the small data set method is applied to calculate the largest Lyapunov exponent to judge the chaotic property of ETF.Then prediction model of ETFTS based on SVM is founded.Finally,the method is applied to predict the time series for the incoming and outgoing passenger flow respectively using ETF data collected in some building.Meanwhile,it is compared with RBF neural network model.Simulation results show that the trend of factual traffic flow is better followed by predictive traffic flow.SVM algorithm has much better prediction performance.The fitting and prediction of ETF with better effect are realized.

Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.

Grain production space reconstruction and land system function tradeoffs in China

Grain production space reconstruction referred to the changes in the quantity,quality and pattern of grain produc-tion space caused by functional tradeoffs and conflicts between grain production space,urban-rural development space,and ecological service space.Exploring tradeoffs between land system functions caused by grain produc-tion space reconstruction was particularly important for ensuring food security,promoting the construction of ecological civilization,and achieving sustainable development.Therefore,this study identified four relationships of land system functions during the process of grain production space reconstruction(1980-2018)in China by using Set Pair Analysis.Research results showed that the reconstruction of grain production space was achieved mainly through three pathways:Grain for Green,deforestation and reclamation,and urban expansion.Generally,ecological service had spatial negative correlation with grain production,economic development and population carrying capacity(P<0.01),but grain production,economic development and population carrying capacity were positively correlated with each other(P<0.01).In the process of grain production space reconstruction,eco-logical services and economic development,ecological services and population carrying capacity had all shown inverse synergies;there was a tradeoffbetween grain production and ecological services,a codirectional tradeoffbetween grain production and economic development,but a strong synergy between economic development and population carrying capacity.However,the functions of land systems only appeared as synergies or tradeoffs,and there were no inverse synergies and codirectional tradeoffs in the separate processes of Grain for Green,deforestation and reclamation,and urban expansion.It can be concluded that the relationships between land system functions were relatively simple in a single process,but it became complex and diverse when multiple processes were integrated for system analysis.

AN ANALYTIC AND APPLICATION TO STATE SPACE RECONSTRUCTION ABOUT CHAOTIC TIME SERIES

The state space, reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: AT. H. Packard, F. Takens, M. Casdagli, J. F. Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time tau were identified. The influence for state space reconstruction of lag time tau was discussed. The result tells us that is a good practical method for state space reconstruction.

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction

A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction.It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay,which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement(AD)in AD algorithm.Thereafter,by means of the iterative algorithm of multiple autocorrelation andΓtest,the near-optimum parameters of embedding dimension and delay time are estimated.This algorithm is provided with a sound theoretic basis,and its computing complexity is relatively lower and not strongly dependent on the data length.The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4%when using conventional algorithm to 1.06%when using this algorithm.The accuracy of invariants in phase space reconstruction is greatly improved.

Deep learning approach to detect seizure using reconstructed phase space images

Epilepsy is a chronic neurological disorder that affects the function of the brain in people of all ages.It manifests in the electroencephalogram(EEG) signal which records the electrical activity of the brain.Various image processing,signal processing,and machine-learning based techniques are employed to analyze epilepsy,using spatial and temporal features.The nervous system that generates the EEG signal is considered nonlinear and the EEG signals exhibit chaotic behavior.In order to capture these nonlinear dynamics,we use reconstructed phase space(RPS) representation of the signal.Earlier studies have primarily addressed seizure detection as a binary classification(normal vs.ictal) problem and rarely as a ternary class(normal vs.interictal vs.ictal)problem.We employ transfer learning on a pre-trained deep neural network model and retrain it using RPS images of the EEG signal.The classification accuracy of the model for the binary classes is(98.5±1.5)% and(95±2)% for the ternary classes.The performance of the convolution neural network(CNN) model is better than the other existing statistical approach for all performance indicators such as accuracy,sensitivity,and specificity.The result of the proposed approach shows the prospect of employing RPS images with CNN for predicting epileptic seizures.

Terrain reconstruction from Chang'e-3 PCAM images

The existing terrain models that describe the local lunar surface have limited resolution and accuracy, which can hardly meet the needs of rover navigation,positioning and geological analysis. China launched the lunar probe Chang＇e-3 in December, 2013. Chang＇e-3 encompassed a lander and a lunar rover called ＂Yutu＂（Jade Rabbit）. A set of panoramic cameras were installed on the rover mast. After acquiring panoramic images of four sites that were explored, the terrain models of the local lunar surface with resolution of 0.02 m were reconstructed. Compared with other data sources, the models derived from Chang＇e-3 data were clear and accurate enough that they could be used to plan the route of Yutu.

Inatorial forecasting method considering macro and micro characteristics of chaotic traffic flow

Traffic flow prediction is an effective strategy to assess traffic conditions and alleviate traffic congestion. Influenced by external non-stationary factors and road network structure, traffic flow sequences have macro spatiotemporal characteristics and micro chaotic characteristics. The key to improving the model prediction accuracy is to fully extract the macro and micro characteristics of traffic flow time sequences. However, traditional prediction model by only considers time features of traffic data, ignoring spatial characteristics and nonlinear characteristics of the data itself, resulting in poor model prediction performance. In view of this, this research proposes an intelligent combination prediction model taking into account the macro and micro features of chaotic traffic data. Firstly, to address the problem of time-consuming and inefficient multivariate phase space reconstruction by iterating nodes one by one, an improved multivariate phase space reconstruction method is proposed by filtering global representative nodes to effectively realize the high-dimensional mapping of chaotic traffic flow. Secondly, to address the problem that the traditional combinatorial model is difficult to adequately learn the macro and micro characteristics of chaotic traffic data, a combination of convolutional neural network(CNN) and convolutional long short-term memory(ConvLSTM) is utilized for capturing nonlinear features of traffic flow more comprehensively. Finally,to overcome the challenge that the combined model performance degrades due to subjective empirical determined network parameters, an improved lightweight particle swarm is proposed for improving prediction accuracy by optimizing model hyperparameters. In this paper, two highway datasets collected by the Caltrans Performance Measurement System(PeMS)are taken as the research objects, and the experimental results from multiple perspectives show that the comprehensive performance of the method proposed in this research is superior to those of the prevalent methods.

Chaotic Characteristic Analysis of Air Traffic System

Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual information,and by embedding dimension which is based on false nearest neighbors method.In order to analyze chaotic characteristics of time series,correlation dimensions and the largest Lyapunov exponents are calculated through Grassberger-Procaccia(G-P)algorithm and small-data method.Five-day radar data from the control center in Guangzhou area are analyzed and the results show that saturated correlation dimensions with self-similar structures exist in time series,and the largest Lyapunov exponents are all equal to zero and not sensitive to initial conditions.Air traffic system is affected by multiple factors,containing inherent randomness,which lead to chaos.Only grasping chaotic characteristics can air traffic be predicted and controlled accurately.

Probability Density Function Method for Observing Reconstructed Attractor Structure

Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

A Novel Method for Nonlinear Time Series Forecasting of Time-Delay Neural Network

Based on the idea of nonlinear prediction of phase space reconstruction, this paper presented a time delay BP neural network model, whose generalization capability was improved by Bayesian regularization. Furthermore, the model is applied to forecast the import and export trades in one industry. The results showed that the improved model has excellent generalization capabilities, which not only learned the historical curve, but efficiently predicted the trend of business. Comparing with common evaluation of forecasts, we put on a conclusion that nonlinear forecast can not only focus on data combination and precision improvement, it also can vividly reflect the nonlinear characteristic of the forecas ting system. While analyzing the forecasting precision of the model, we give a model judgment by calculating the nonlinear characteristic value of the combined serial and original serial, proved that the forecasting model can reasonably catch＇ the dynamic characteristic of the nonlinear system which produced the origin serial.

An efficient method of distinguishing chaos from noise

It is an important problem in chaos theory whether an observed irregular signal is deterministic chaotic or stochas- tic. We propose an efficient method for distinguishing deterministic chaotic from stochastic time series for short scalar time series. We first investigate, with the increase of the embedding dimension, the changing trend of the distance between two points which stay close in phase space. And then, we obtain the differences between Gaussian white noise and deterministic chaotic time series underlying this method. Finally, numerical experiments are presented to testify the validity and robustness of the method. Simulation results indicate that our method can distinguish deterministic chaotic from stochastic time series effectively even when the data are short and contaminated.

Nonlinear chaotic characteristic in leaching process and prediction of leaching cycle period

A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space reconstruction for time series of monitoring data, the saturated embedding dimension and the correlation dimension were obtained, and the evolution laws between neighboring points in the reconstructed phase space were revealed. With BP neural network, a prediction model of concentration of leaching solution was set up and the maximum error of which was less than 2%. The results show that there exist chaotic characteristics in leaching system, and samples of different grades have different nonlinear dynamic features; the higher the grade of sample, the smaller the correlation dimension; furthermore, the maximum Lyapunov index, energy dissipation and chaotic extent of the leaching system increase with grade of the sample; by phase space reconstruction, the subtle change features of concentration of leaching solution can be magnified and the inherent laws can be fully demonstrated. According to the laws, a prediction model of leaching cycle period has been established to provide a theoretical foundation for solution mining.

Low dimensional chaos in the AT and GC skew profiles of DNA sequences

This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.

KLT-based local linear prediction of chaotic time series

In the reconstructed phase space, based on the Karhunen-Loeve transformation （KLT）, the new local linear prediction method is proposed to predict chaotic time series. ＆ noise-free chaotic time series and a noise added chaotic time series are analyzed. The simulation results show that the KLT-based local linear prediction method can effectively make one-step and multi-step prediction for chaotic time series, and the one-step and multi-step prediction accuracies of the KLT-based local linear prediction method are superior to that of the traditional local linear prediction.

Selection of Optimal Embedding Parameters Applied to Short and Noisy Time Series from Rossler System

Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the R&ouml;ssler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.